156 in Binary
2026-02-21 20:39 Diff
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156 can be converted easily from decimal to binary. The methods mentioned below will help us convert the number. Let’s see how it is done.

Expansion Method: Let us see the step-by-step process of converting 156 using the expansion method.

Step 1 - Figure out the place values: In the binary system, each place value is a power of 2. Therefore, in the first step, we will ascertain the powers of 2. 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 Since 128 is less than 156, we stop at 2^7 = 128.

Step 2 - Identify the largest power of 2: In the previous step, we stopped at 2^7 = 128. This is because in this step, we have to identify the largest power of 2, which is less than or equal to the given number, 156. Since 2^7 is the number we are looking for, write 1 in the 2^7 place. Now the value of 2^7, which is 128, is subtracted from 156. 156 - 128 = 28.

Step 3 - Identify the next largest power of 2: In this step, we need to find the largest power of 2 that fits into the result of the previous step, 28. So, the next largest power of 2 is 2^4, which is less than or equal to 28. Now, we have to write 1 in the 2^4 place. And then subtract 16 from 28. 28 - 16 = 12.

Step 4 - Continue the process: The next largest power of 2 that fits into 12 is 2^3, so write 1 in the 2^3 place and subtract 8 from 12. 12 - 8 = 4. Finally, the largest power of 2 that fits into 4 is 2^2, so write 1 in the 2^2 place and subtract 4 from 4. 4 - 4 = 0. We need to stop the process here since the remainder is 0.

Step 5 - Identify the unused place values: In step 2, step 3, and step 4, we wrote 1 in the 2^7, 2^4, 2^3, and 2^2 places. Now, we can just write 0s in the remaining places, which are 2^6, 2^5, 2^1, and 2^0. Now, by substituting the values, we get, 0 in the 2^0 place 0 in the 2^1 place 1 in the 2^2 place 1 in the 2^3 place 1 in the 2^4 place 0 in the 2^5 place 0 in the 2^6 place 1 in the 2^7 place

Step 6 - Write the values in reverse order: We now write the numbers upside down to represent 156 in binary. Therefore, 10011100 is 156 in binary.

Grouping Method: In this method, we divide the number 156 by 2. Let us see the step-by-step conversion.

Step 1 - Divide the given number 156 by 2. 156 / 2 = 78. Here, 78 is the quotient and 0 is the remainder.

Step 2 - Divide the previous quotient (78) by 2. 78 / 2 = 39. Here, the quotient is 39 and the remainder is 0.

Step 3 - Repeat the previous step. 39 / 2 = 19. Now, the quotient is 19, and 1 is the remainder.

Step 4 - Repeat the previous step. 19 / 2 = 9. Here, the quotient is 9, and 1 is the remainder.

Step 5 - Continue dividing. 9 / 2 = 4. The quotient is 4, and the remainder is 1. Step 6 - Continue dividing. 4 / 2 = 2. The quotient is 2, and the remainder is 0.

Step 7 - Continue dividing. 2 / 2 = 1. The quotient is 1, and the remainder is 0.

Step 8 - Continue dividing. 1 / 2 = 0. Here, the quotient is 0, and the remainder is 1. We stop the division here because the quotient is 0.

Step 9 - Write down the remainders from bottom to top. Therefore, 156 (decimal) = 10011100 (binary).